Solve for $x$ and $y$ using elimination. ${-x+3y = -2}$ ${x-4y = 1}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-y = -1$ $\dfrac{-y}{{-1}} = \dfrac{-1}{{-1}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {-x+3y = -2}\thinspace$ to find $x$ ${-x + 3}{(1)}{= -2}$ $-x+3 = -2$ $-x+3{-3} = -2{-3}$ $-x = -5$ $\dfrac{-x}{{-1}} = \dfrac{-5}{{-1}}$ ${x = 5}$ You can also plug ${y = 1}$ into $\thinspace {x-4y = 1}\thinspace$ and get the same answer for $x$ : ${x - 4}{(1)}{= 1}$ ${x = 5}$